Math Problem: Synthetic Division

Discus: SAT/ACT Tests and Test Preparation: October 2003 Archive: Math Problem: Synthetic Division
 By Phantom (Phantom) on Thursday, October 02, 2003 - 04:37 pm: Edit

Another math problem (you will find this less intriguing then my last math problem, no doubt):

Find the quotient and remainder of:
3x^4-2x^3+5x^2+x+1 divided by x^2+2x

The long division way comes out 3x^2-8x+21 remainder -41x+1, which is the right answer.
However, when I then tried to use the synthetic division method, the answer was 3x^2-8x+21 remainder -41x+83.

My work:
x^2+2x becomes x(x+2) or (x-0)(x+2)

-2| 3 -2 5 1 1
-6 16 -42 82
--------------------------
3 -8 21 -41 83

*the -6 is lined up under 3, 16 under -2, etc.

And then you can continue with 0 instead of -2 which results in the same thing.

What am I doing wrong? Why is the remainder

 By Phantom (Phantom) on Thursday, October 02, 2003 - 04:46 pm: Edit

By the way, my teacher had a look and he said that both answers are right. Is that correct? I multiplied my quotient and divisor together and added the remainder to them and while the one with -41x+1 comes out to be the original equation, the second remainder doesn't work.

Also, I don't know if it's possible to suggest things on this forum, but I think that there should be a separate "homework help" category.

 By Phantom (Phantom) on Thursday, October 02, 2003 - 05:28 pm: Edit

actually, i know what im doing wrong--by doing the division with only -2, I'm ignoring the extra x. But then how do u incorporate the x?

 By Becks777 (Becks777) on Thursday, October 02, 2003 - 05:33 pm: Edit

if this is a sat or sat ii problem just plug in any number for x and then divide..........as simple as that!

 By Phantom (Phantom) on Thursday, October 02, 2003 - 05:36 pm: Edit

no, this is a school problem (no multiple choice) and it's the synthetic division unit so I need to know how it works.

 By Mo222 (Mo222) on Thursday, October 02, 2003 - 05:44 pm: Edit

Synthetic division must be (some expression)/(x-k) -- you dont have a # in the form (x-k) so you have to use polynomial long division

 By Phantom (Phantom) on Thursday, October 02, 2003 - 05:53 pm: Edit

so there's no way to do synthetic if the divisor's x^2+2x?
not even if the x is factored out? I don't understand why (x-0) won't work (if you put 0 in the box).

 By Phantom (Phantom) on Thursday, October 02, 2003 - 06:22 pm: Edit

i'm sorry, when I said:

*the -6 is lined up under 3, 16 under -2, etc.

I really meant that -6 was lined up under -2, and so on.

 By Montydsw11 (Montydsw11) on Thursday, October 02, 2003 - 06:59 pm: Edit

synthetic only works for linear factors